Database normalization


Database normalization is the process of structuring a relational database in accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity. It was first proposed by Edgar F. Codd as part of his relational model.
Normalization entails organizing the columns and tables of a database to ensure that their dependencies are properly enforced by database integrity constraints. It is accomplished by applying some formal rules either by a process of synthesis or decomposition.

Objectives

A basic objective of the first normal form defined by Codd in 1970 was to permit data to be queried and manipulated using a "universal data sub-language" grounded in first-order logic.
The objectives of normalization beyond 1NF were stated as follows by Codd:
When an attempt is made to modify a relation, the following undesirable side-effects may arise in relations that have not been sufficiently normalized:
A fully normalized database allows its structure to be extended to accommodate new types of data without changing existing structure too much. As a result, applications interacting with the database are minimally affected.
Normalized relations, and the relationship between one normalized relation and another, mirror real-world concepts and their interrelationships.

Example

Querying and manipulating the data within a data structure that is not normalized, such as the following non-1NF representation of customers' credit card transactions, involves more complexity than is really necessary:
CustomerCust. IDTransactions---
Abraham1
To each customer corresponds a 'repeating group' of transactions. The automated evaluation of any query relating to customers' transactions, therefore, would broadly involve two stages:
  1. Unpacking one or more customers' groups of transactions allowing the individual transactions in a group to be examined, and
  2. Deriving a query result based on the results of the first stage
For example, in order to find out the monetary sum of all transactions that occurred in October 2003 for all customers, the system would have to know that it must first unpack the Transactions group of each customer, then sum the Amounts of all transactions thus obtained where the Date of the transaction falls in October 2003.
One of Codd's important insights was that structural complexity can be reduced. Reduced structural complexity gives users, applications, and DBMSs more power and flexibility to formulate and evaluate the queries. A more normalized equivalent of the structure above might look like this:
Cust. IDTr. IDDateAmount
11289014-Oct-2003−87
11290415-Oct-2003−50
21289814-Oct-2003−21
31290715-Oct-2003−18
31492020-Nov-2003−70
31500327-Nov-2003−60

In the modified structure, the primary key is in the first relation, in the second relation.
Now each row represents an individual credit card transaction, and the DBMS can obtain the answer of interest, simply by finding all rows with a Date falling in October, and summing their Amounts. The data structure places all of the values on an equal footing, exposing each to the DBMS directly, so each can potentially participate directly in queries; whereas in the previous situation some values were embedded in lower-level structures that had to be handled specially. Accordingly, the normalized design lends itself to general-purpose query processing, whereas the unnormalized design does not. The normalized version also allows the user to change the customer name in one place and guards against errors that arise if the customer name is misspelled on some records.

Normal forms

Codd introduced the concept of normalization and what is now known as the first normal form in 1970. Codd went on to define the second normal form and third normal form in 1971, and Codd and Raymond F. Boyce defined the Boyce-Codd normal form in 1974.
Informally, a relational database relation is often described as "normalized" if it meets third normal form. Most 3NF relations are free of insertion, update, and deletion anomalies.
The normal forms are:
UNF
1NF
2NF
3NF
EKNF
BCNF
4NF
ETNF
5NF
DKNF
6NF
Primary key
No repeating groups
Atomic columns
Every non-trivial functional dependency either does not begin with a proper subset of a candidate key or ends with a prime attribute
Every non-trivial functional dependency begins with a superkey or ends with a prime attribute
Every non-trivial functional dependency either begins with a superkey or ends with an elementary prime attribute
Every non-trivial functional dependency begins with a superkey
Every non-trivial multivalued dependency begins with a superkey
Every join dependency has a superkey component
Every join dependency has only superkey components
Every constraint is a consequence of domain constraints and key constraints
Every join dependency is trivial

Example of a step by step normalization

Normalization is a database design technique, which is used to design a relational database table up to higher normal form. The process is progressive, and a higher level of database normalization cannot be achieved unless the previous levels have been satisfied.
That means that, having data in unnormalized form and aiming to achieve the highest level of normalization, the first step would be to ensure compliance to first normal form, the second step would be to ensure second normal form is satisfied, and so forth in order mentioned above, until the data conform to sixth normal form.
However, it is worth noting that normal forms beyond 4NF are mainly of academic interest, as the problems they exist to solve rarely appear in practice.
Please note that the data in the following example were intentionally designed to contradict most of the normal forms. In real life, it's quite possible to be able to skip some of the normalization steps because the table doesn't contain anything contradicting the given normal form. It also commonly occurs that fixing a violation of one normal form also fixes a violation of a higher normal form in the process. Also one table has been chosen for normalization at each step, meaning that at the end of this example process, there might still be some tables not satisfying the highest normal form.

Initial data

Let a database table with the following structure:
TitleAuthorAuthor NationalityFormatPriceSubjectPagesThicknessPublisherPublisher CountryPublication TypeGenre IDGenre Name
Beginning MySQL Database Design and OptimizationChad RussellAmericanHardcover49.99MySQL,
Database,
Design		520ThickApressUSAE-book1Tutorial

We assume in this example that each book has only one author.

Satisfying 1NF

To satisfy 1NF, the values in each column of a table must be atomic. In the initial table, Subject contains a set of subject values, meaning it does not comply.
One way to achieve the 1NF would be to separate the duplicities into multiple columns using repeating groups Subject:
TitleFormatAuthorAuthor NationalityPriceSubject 1Subject 2Subject 3PagesThicknessPublisherPublisher countryGenre IDGenre Name
Beginning MySQL Database Design and OptimizationHardcoverChad RussellAmerican49.99MySQLDatabaseDesign520ThickApressUSA1Tutorial

Although now the table formally complies to the 1NF, the problem with this solution is obvious - if a book has more than three subjects, it cannot be added to the database without altering its structure.
To solve the problem in a more elegant way, it is necessary to identify entities represented in the table and separate them into their own respective tables. In this case, it would result in Book, Subject and Publisher tables:
TitleFormatAuthorAuthor NationalityPricePagesThicknessGenre IDGenre NamePublisher ID
Beginning MySQL Database Design and OptimizationHardcoverChad RussellAmerican49.99520Thick1Tutorial1

Simply separating the initial data into multiple tables would break the connection between the data. That means the relationships between the newly introduced tables need to be determined. Notice that the Publisher ID column in the Book's table is a foreign key realizing many-to-one relation between a book and a publisher.
A book can fit many subjects, as well as a subject may correspond to many books. That means also a many-to-many relationship needs to be defined, achieved by creating a link table:

Instead of one table in unnormalized form, there are now 4 tables conforming to the 1NF.

Satisfying 2NF

The Book table has one candidate key, the compound key '. Consider the following table fragment:
TitleFormatAuthorAuthor NationalityPricePagesThicknessGenre IDGenre NamePublisher ID
Beginning MySQL Database Design and OptimizationHardcoverChad RussellAmerican49.99520Thick1Tutorial1
Beginning MySQL Database Design and OptimizationE-bookChad RussellAmerican22.34520Thick1Tutorial1
The Relational Model for Database Management: Version 2E-bookE.F.CoddBritish13.88538Thick2Popular science2
The Relational Model for Database Management: Version 2PaperbackE.F.CoddBritish39.99538Thick2Popular science2

All of the attributes that are not part of the candidate key depend on Title, but only Price also depends on Format. To conform to 2NF and remove duplicities, every non candidate-key attribute must depend on the whole candidate key, not just part of it.
To normalize this table, make ' a candidate key so that every non candidate-key attribute depends on the whole candidate key, and remove Price into a separate table so that its dependency on Format can be preserved:

Now, the Book table conforms to 2NF.

Satisfying 3NF

A table in third normal form is a table in 2NF that has no transitive dependencies. Note the Book table with more rows :
TitleAuthorAuthor NationalityPagesThicknessGenre IDGenre NamePublisher ID
Beginning MySQL Database Design and OptimizationChad RussellAmerican520Thick1Tutorial1
The Relational Model for Database Management: Version 2E.F.CoddBritish538Thick2Popular science2
Learning SQLAlan BeaulieuAmerican338Slim1Tutorial3
SQL CookbookAnthony MolinaroAmerican636Thick1Tutorial3

Genre ID and Genre Name both depend on the primary key , but they are not independent of one another. The dependency of, say, Genre Name on the primary key can be deduced from the dependency of Genre Name on Genre ID and of Genre ID on the primary key. Since there are more titles than genres, that dependency introduces redundant data into the Book table which can be eliminated by abstracting the dependency of Genre Name on Genre ID into its own table:

The Book table is now in third normal form. Although tables in 1NF are by definition normalized, "normalized" is commonly used to mean 3NF.

Satisfying EKNF

The elementary key normal form falls strictly between 3NF and BCNF and is not much discussed in the literature. It is intended “to capture the salient qualities of both 3NF and BCNF” while avoiding the problems of both. Since it is rarely mentioned in literature, it is not included in this example.

Satisfying BCNF

A relational schema R is considered to be in Boyce–Codd normal form if, for every one of its dependencies X → Y, one of the following conditions hold true:
  • X → Y is a trivial functional dependency
  • X is a superkey for schema R
Consider the table in 3NF from the previous step:
TitleAuthorAuthor NationalityPagesThicknessGenre IDPublisher ID
Beginning MySQL Database Design and OptimizationChad RussellAmerican520Thick11
The Relational Model for Database Management: Version 2E.F.CoddBritish538Thick22
Learning SQLAlan BeaulieuAmerican338Slim13
SQL CookbookAnthony MolinaroAmerican636Thick13

There is a non-trivial dependency violating BCNF - → . Therefore, the table should be decomposed:

Now, each attribute represents a fact about the key, the whole key, and nothing but the key. Therefore BCNF has been achieved.

Satisfying 4NF

Assume the database is owned by a book retailer franchise that has several franchisees that own shops in different locations. And therefore the retailer decided to add a table that contains data about availability of the books at different locations:
Franchisee IDTitleLocation
1Beginning MySQL Database Design and OptimizationCalifornia
1Beginning MySQL Database Design and OptimizationFlorida
1Beginning MySQL Database Design and OptimizationTexas
1The Relational Model for Database Management: Version 2California
1The Relational Model for Database Management: Version 2Florida
1The Relational Model for Database Management: Version 2Texas
2Beginning MySQL Database Design and OptimizationCalifornia
2Beginning MySQL Database Design and OptimizationFlorida
2Beginning MySQL Database Design and OptimizationTexas
2The Relational Model for Database Management: Version 2California
2The Relational Model for Database Management: Version 2Florida
2The Relational Model for Database Management: Version 2Texas
3Beginning MySQL Database Design and OptimizationTexas

As this table structure consists of a compound primary key, it doesn't contain any non-key attributes and it's already in BCNF. However, if we assume that all available books are offered in each area, we might notice that the Title is not unambiguously bound to a certain Location and therefore the table doesn't satisfy 4NF.
That means that, to satisfy the fourth normal form, this table needs to be decomposed as well:

Now, every record is unambiguously identified by a superkey, therefore 4NF is satisfied.

Satisfying ETNF

Suppose the franchisees can also order books from different suppliers. Let the relation also be subject to the following constraint:
  • If a certain supplier supplies a certain title
  • and the title is supplied to the franchisee
  • and the franchisee is being supplied by the supplier,
  • then the supplier supplies the title to the franchisee.
Supplier IDTitleFranchisee ID
1Beginning MySQL Database Design and Optimization1
2The Relational Model for Database Management: Version 22
3Learning SQL3

This table is in 4NF, but the Supplier ID is equal to the join of its projections: . No component of that join dependency is a superkey, so the table does not satisfy the ETNF and can be further decomposed:

The decomposition produces ETNF compliance.

Satisfying 5NF

To spot a table not satisfying the 5NF, it is usually necessary to examine the data thoroughly. Suppose the table from 4NF example with a little modification in data and let's examine if it satisfies 5NF:
Franchisee IDTitleLocation
1Beginning MySQL Database Design and OptimizationCalifornia
1Learning SQLCalifornia
1The Relational Model for Database Management: Version 2Texas
2The Relational Model for Database Management: Version 2California

If we decompose this table, we lower redundancies and get the following two tables:

What happens if we try to join these tables? The query would return the following data:
Franchisee IDTitleLocation
1Beginning MySQL Database Design and OptimizationCalifornia
1Learning SQLCalifornia
1The Relational Model for Database Management: Version 2California
1The Relational Model for Database Management: Version 2Texas
1Learning SQLTexas
1Beginning MySQL Database Design and OptimizationTexas
2The Relational Model for Database Management: Version 2California

Apparently, the JOIN returns three more rows than it should - let's try to add another table to clarify the relation. We end up with three separate tables:



What will the JOIN return now? It actually is not possible to join these three tables. That means it wasn't possible to decompose the Franchisee - Book Location without data loss, therefore the table already satisfies 5NF.
C.J. Date has argued that only a database in 5NF is truly "normalized".

Satisfying DKNF

Let's have a look at the Book table from previous examples and see if it satisfies the Domain-key normal form:
TitlePagesThicknessGenre IDPublisher ID
Beginning MySQL Database Design and Optimization520Thick11
The Relational Model for Database Management: Version 2538Thick22
Learning SQL338Slim13
SQL Cookbook636Thick13

Logically, Thickness is determined by number of pages. That means it depends on Pages which is not a key. Let's set an example convention saying a book up to 350 pages is considered "slim" and a book over 350 pages is considered "thick".
This convention is technically a constraint but it is neither a domain constraint nor a key constraint; therefore we cannot rely on domain constraints and key constraints to keep the data integrity.
In other words - nothing prevents us from putting, for example, "Thick" for a book with only 50 pages - and this makes the table violate DKNF.
To solve this, we can create a table holding enumeration that defines the Thickness and remove that column from the original table:

That way, the domain integrity violation has been eliminated, and the table is in DKNF.

Satisfying 6NF

A simple and intuitive definition of the sixth normal form is that "a table is in 6NF when the row contains the Primary Key, and at most one other attribute".
That means, for example, the Publisher table designed while [|creating the 1NF]
needs to be further decomposed into two tables:
The obvious drawback of 6NF is the proliferation of tables required to represent the information on a single entity. If a table in 5NF has one primary key column and N attributes, representing the same information in 6NF will require N tables; multi-field updates to a single conceptual record will require updates to multiple tables; and inserts and deletes will similarly require operations across multiple tables. For this reason, in databases intended to serve Online Transaction Processing needs, 6NF should not be used.
However, in data warehouses, which do not permit interactive updates and which are specialized for fast query on large data volumes, certain DBMSs use an internal 6NF representation - known as a Columnar data store. In situations where the number of unique values of a column is far less than the number of rows in the table, column-oriented storage allow significant savings in space through data compression. Columnar storage also allows fast execution of range queries
In all these cases, however, the database designer does not have to perform 6NF normalization manually by creating separate tables. Some DBMSs that are specialized for warehousing, such as Sybase IQ, use columnar storage by default, but the designer still sees only a single multi-column table. Other DBMSs, such as Microsoft SQL Server 2012 and later, let you specify a "columnstore index" for a particular table.
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